Whole tone

A whole tone is an interval that is the size of a major second that functions as the large step of a diatonic scale.

Whole tones range roughly from 160 to 240 cents, and are preferably closer to 200 cents. Whole tones may be defined to be between ~165 and ~250 cents (1\3edP4 and 1\2edP4), based on the definition of a diatonic tetrachord.

Sometimes, the term whole tone refers specifically to the interval 9/8 (the Pythagorean major second), or to the intervals 9/8 and 10/9 together (the two sizes of whole tone in the Zarlino diatonic scale). These two sizes of whole tone are separated by a syntonic comma, which is tempered out in meantone temperament. Therefore, meantone has a single whole tone in between 9/8 and 10/9 in size, hence the name. In 12edo, the whole tone divides the octave into six, and as a result whole-tone-generated scales are generally 6-form.

Name

Whole tone comes from diatonic scale theory, which comprises the diatonic scale of five whole tones and two semitones; the step ratio of diatonic is either exactly or roughly 2:1 in most historical tunings, thus a semitone is roughly half of a whole tone. This is not to be confused with the sense of tone to refer to a note.

Qualities

While the whole tone is itself a quality of second (the major second), the various commatic inflections are considered by some theorists to represent subqualities of whole tone; 9/8 is the "major tone" and 10/9 the "minor tone".

As generators of temperaments

The most prominent whole-tone-generated temperament is didacus, which is a no-threes subgroup temperament generated by a whole tone of about 194 cents that finds 5/4 at 2 steps and 7/4 at 5 steps; this is the most obvious temperament interpretation of the 12edo whole-tone scale. Didacus is a 6 cluster temperament.

Another notable whole tone temperament is machine, where a ~215c whole tone, interpreted as a very flat 8/7 or a sharp 9/8, stacks three times to 16/11. A more accurate but more complex interpretation is contraption, which instead finds 7/4 at 10 steps as a 2.7.11 subgroup temperament. 11edo supports both temperaments, and in fact contraption is an 11-form temperament. In either case, the generator may be interpreted as 17/15 and 6 steps (octave-reduced) as a flat 17/16, so that they extend to 2.15.7.11.17.

Additional temperaments associated with whole tone generators include tetracot (which stacks a flat 10/9 four times to reach 3/2), and slendric (which stacks a just or slightly sharpened 8/7 three times to reach 3/2). The edges of the tetrachordal definition mentioned above represent porcupine (equalizing 9:10:11:12) and semaphore (equalizing 6:7:8).

In just intonation

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